The bigger picture of textual data
The first challenge of NLP is text quantification.
An introduction to statistical natural language processing in R
All materials: https://github.com/ben-aaron188/snlp
Ask all your questions
quanteda package## [1] '4.1.0'
Aspects of textual data
The whole situation makes me very anxious. I do not believe, as a country, we are doing everything to prevent the spread. I believe we should be in a full and proper lockdown like other countries. I fear for my children and their futures.
Numerical summaries of units of a document or collection of documents.
Examples:
Information about the arrangement/structure of language.
Examples:
Information of the text concerned with meaning.
Units of textual data
Example sentence:
The whole situation makes me very anxious.
## Tokens consisting of 1 document.
## text1 :
## [1] "The" "whole" "situation" "makes" "me" "very"
## [7] "anxious" "."
Removing punctuation:
toks_no_punct = tokens(text_1
, remove_punct = T
, remove_numbers = F
, remove_url = F
, remove_separators = F)
toks_no_punct## Tokens consisting of 1 document.
## text1 :
## [1] "The" " " "whole" " " "situation" " "
## [7] "makes" " " "me" " " "very" " "
## [ ... and 1 more ]
This is far from a solved problem:
## Tokens consisting of 1 document.
## text1 :
## [1] "evidence-based" "self-fulfilling" "prophesy"
## Tokens consisting of 1 document.
## text1 :
## [1] "evidence" "-" "based" "self" "-"
## [6] "fulfilling" "prophesy"
## [1] 1
## text1
## 8
## [1] 42
Text metrics (corpus statistics)
Common text metrics: readability (see
quanteda.textstats), lexical diversity
Example 1:
I am very anxious about this situation. Very anxious.
Example 2:
I am very anxious about this situation. Really scary.
Which has a higher lexical diversity?
ex_1 = 'I am very anxious about this situation. Very anxious.'
ex_2 = 'I am very anxious about this situation. Really scary.'The type-token ration (TTR) is often used as a measure of lexical diversity.
## text1
## 0.8181818
## text1
## 0.9090909
Handling textual data in R
stringr packagecorpus objectA collection of documents is a corpus.
Quanteda assumes you work with corpus objects.
data_1 = fread('/Users/bennettkleinberg/GitHub/snlp/data/real_world_worry_waves_dataset.csv')
names(data_1)[1:13]## [1] "id" "prolific_id" "worry_wave1"
## [4] "chosen_emotion_wave1" "anger_wave1" "disgust_wave1"
## [7] "fear_wave1" "anxiety_wave1" "sadness_wave1"
## [10] "happiness_wave1" "relaxation_wave1" "desire_wave1"
## [13] "text_long_wave1"
## Corpus consisting of 1,152 documents.
## text1 :
## "I am more worried about getting access to my normal healthca..."
##
## text2 :
## "I am a little concerned that so many people are not staying ..."
##
## text3 :
## "I feel relaxed. I'm aware of the risks and I'm doing my very..."
##
## text4 :
## "I feel a little stressed by it all, I would like to go outsi..."
##
## text5 :
## "I am fed up about not being able to go out when I want, I mi..."
##
## text6 :
## "At this very moment, I am feeling very fearful and sad about..."
##
## [ reached max_ndoc ... 1,146 more documents ]
## Corpus consisting of 1152 documents, showing 10 documents:
##
## Text Types Tokens Sentences
## text1 89 132 6
## text2 70 106 5
## text3 72 114 6
## text4 71 108 4
## text5 71 117 5
## text6 68 120 6
## text7 73 118 2
## text8 65 109 5
## text9 91 136 3
## text10 88 124 4
Text representations
A numerical representation of textual data.
Most common approach:
I think I believe him
How can we construct a term-frequency table?
| text_id | I | think | believe | him |
|---|---|---|---|---|
| text1 | 2 | 1 | 1 | 1 |
quantedatokens or corpus objects, create a
DFM tableex_3 = 'I think I believe him'
corpus_ex_3 = corpus(ex_3)
tokens_ex_3 = tokens(corpus_ex_3)
dfm(tokens_ex_3
, tolower = T)## Document-feature matrix of: 1 document, 4 features (0.00% sparse) and 0 docvars.
## features
## docs i think believe him
## text1 2 1 1 1
Sparsity = % of zero-cells
corpus_3 = corpus(c("I think I believe him", "This is a cool function"))
tokens_corpus_3 = tokens(corpus_3)## Document-feature matrix of: 2 documents, 9 features (50.00% sparse) and 0 docvars.
## features
## docs i think believe him this is a cool function
## text1 2 1 1 1 0 0 0 0 0
## text2 0 0 0 0 1 1 1 1 1
What happens if we add bi-grams (i.e., \(n=1\) and \(n=2\))?
I think I believe him
## Tokens consisting of 1 document.
## text1 :
## [1] "I" "think" "I" "believe" "him"
## [6] "I_think" "think_I" "I_believe" "believe_him"
So we very quickly run into dimensionality problems with text data.
Unigrams (~ tokens)
tokens_corpus_rwwd = tokens(corpus_rwwd)
dfm_unigrams = dfm(tokens_ngrams(tokens_corpus_rwwd
, n = 1)
, tolower = T)
dfm_unigrams## Document-feature matrix of: 1,152 documents, 6,274 features (98.71% sparse) and 0 docvars.
## features
## docs i am more worried about getting access to my normal
## text1 7 3 1 1 2 1 1 5 5 1
## text2 3 2 0 1 0 0 0 3 0 0
## text3 6 0 0 0 2 0 0 5 3 0
## text4 4 0 0 0 0 0 0 6 1 2
## text5 7 2 1 1 1 0 0 7 4 0
## text6 7 3 0 1 4 0 0 2 3 0
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 6,264 more features ]
## Document-feature matrix of: 1,152 documents, 150,549 features (99.79% sparse) and 0 docvars.
## features
## docs i am more worried about getting access to my normal
## text1 7 3 1 1 2 1 1 5 5 1
## text2 3 2 0 1 0 0 0 3 0 0
## text3 6 0 0 0 2 0 0 5 3 0
## text4 4 0 0 0 0 0 0 6 1 2
## text5 7 2 1 1 1 0 0 7 4 0
## text6 7 3 0 1 4 0 0 2 3 0
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 150,539 more features ]
## Document-feature matrix of: 10 documents, 10 features (86.00% sparse) and 0 docvars.
## features
## docs a_walk walk_, ,_but but_that that_is is_not not_possible possible_right
## text1 1 1 1 1 1 1 1 1
## text2 0 0 0 0 0 0 0 0
## text3 0 0 0 0 0 0 0 0
## text4 0 0 0 0 0 1 0 0
## text5 0 0 0 0 0 0 0 0
## text6 0 0 0 0 0 0 0 0
## features
## docs right_now now_.
## text1 1 1
## text2 0 0
## text3 0 0
## text4 0 0
## text5 0 0
## text6 0 0
## [ reached max_ndoc ... 4 more documents ]
Reducing dimensionality in DFM representations
But: not all words (ngrams) are equally important.
## . i the and to , ._i my of a is am that
## 6464 6049 5842 5234 4369 2966 2344 2289 2091 2035 1928 1775 1769
## it i_am in for as about this
## 1715 1669 1628 1567 1429 1410 1346
These add little information.
Also known as stopwords and often removed in preprocessing.
Common stopword lists:
## [1] "i" "me" "my" "myself" "we"
## [6] "our" "ours" "ourselves" "you" "your"
## [11] "yours" "yourself" "yourselves" "he" "him"
## [16] "his" "himself" "she" "her" "hers"
Note: no universal agreement on stopwords!
tokens_rwwd = tokens_select(tokens_corpus_rwwd
, pattern = stopwords("en")
, selection = "remove")
dfm(tokens_ngrams(tokens_rwwd
, n = 1:3)
, tolower = T)## Document-feature matrix of: 1,152 documents, 113,954 features (99.85% sparse) and 0 docvars.
## features
## docs worried getting access normal healthcare moment , concerned corona .
## text1 1 1 1 1 1 1 6 1 1 5
## text2 1 0 0 0 0 0 2 1 0 5
## text3 0 0 0 0 0 0 3 0 0 6
## text4 0 0 0 2 0 0 5 0 0 4
## text5 1 0 0 0 0 0 4 0 0 4
## text6 1 0 0 0 0 1 2 0 1 6
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 113,944 more features ]
Take these example:
These all belong to the same “core”.
Stemming and lemmatisation can solve this.
Idea: reduce a word to its word stem. Works by removing suffixes.
## Tokens consisting of 1 document.
## text1 :
## [1] "The" "whole" "situation" "makes" "me" "very"
## [7] "anxious" "."
## Tokens consisting of 1 document.
## text1 :
## [1] "The" "whole" "situat" "make" "me" "veri" "anxious"
## [8] "."
## Tokens consisting of 1 document.
## text1 :
## [1] "creat" "creat" "creat"
## Tokens consisting of 1 document.
## text1 :
## [1] "gone" "went" "go" "goe"
Idea: reduce a word to its root meaning (the lemma)
## [1] "go" "go" "go" "go"
The RWWD dataset:
dfm_stopw = dfm(tokens_ngrams(tokens_rwwd
, n = 1:3)
, tolower = T)
dfm_red = dfm_wordstem(x = dfm_stopw)
dfm_red## Document-feature matrix of: 1,152 documents, 106,412 features (99.84% sparse) and 0 docvars.
## features
## docs worri get access normal healthcar moment , concern corona .
## text1 1 2 1 1 1 1 6 1 1 5
## text2 1 1 0 0 0 0 2 1 0 5
## text3 0 0 0 0 0 0 3 1 0 6
## text4 0 2 0 2 0 0 5 0 0 4
## text5 1 1 0 0 0 0 4 0 0 4
## text6 1 0 0 0 0 1 2 0 1 6
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 106,402 more features ]
We still have high sparsity: 106,412 features (99.84% sparse)
Ideas?
Trimming the DFM based on term- or document-frequencies:
## Document-feature matrix of: 1,152 documents, 260 features (87.51% sparse) and 0 docvars.
## features
## docs worri get normal moment , concern corona . health even
## text1 1 2 1 1 6 1 1 5 1 1
## text2 1 1 0 0 2 1 0 5 0 0
## text3 0 0 0 0 3 1 0 6 0 0
## text4 0 2 2 0 5 0 0 4 0 0
## text5 1 1 0 0 4 0 0 4 0 0
## text6 1 0 0 1 2 0 1 6 2 0
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 250 more features ]
We assume all words are equally important.
But:
We want to:
Metric for word importance: frequency of term \(t\) in document \(d\)
## Document-feature matrix of: 10 documents, 10 features (54.00% sparse) and 0 docvars.
## features
## docs worri get normal moment , concern
## text1 0.02040816 0.04081633 0.02040816 0.02040816 0.12244898 0.02040816
## text2 0.02222222 0.02222222 0 0 0.04444444 0.02222222
## text3 0 0 0 0 0.07894737 0.02631579
## text4 0 0.04081633 0.04081633 0 0.10204082 0
## text5 0.02325581 0.02325581 0 0 0.09302326 0
## text6 0.01694915 0 0 0.01694915 0.03389831 0
## features
## docs corona . health even
## text1 0.02040816 0.10204082 0.02040816 0.02040816
## text2 0 0.11111111 0 0
## text3 0 0.15789474 0 0
## text4 0 0.08163265 0 0
## text5 0 0.09302326 0 0
## text6 0.01694915 0.10169492 0.03389831 0
## [ reached max_ndoc ... 4 more documents ]
## Document-feature matrix of: 10 documents, 10 features (54.00% sparse) and 0 docvars.
## features
## docs worri get normal moment , concern corona . health even
## text1 1 2 1 1 6 1 1 5 1 1
## text2 1 1 0 0 2 1 0 5 0 0
## text3 0 0 0 0 3 1 0 6 0 0
## text4 0 2 2 0 5 0 0 4 0 0
## text5 1 1 0 0 4 0 0 4 0 0
## text6 1 0 0 1 2 0 1 6 2 0
## [ reached max_ndoc ... 4 more documents ]
## worri get normal moment , concern corona . health even
## 673 487 216 184 894 213 104 1138 272 146
Trick: inverse document-frequency
\(idf(t) = \frac{n}{df(d, t)}\) for \(n\) documents in the corpus.
When \(n\) becomes really large…
## Document-feature matrix of: 10 documents, 10 features (54.00% sparse) and 0 docvars.
## features
## docs worri get normal moment , concern corona . health even
## text1 1 2 1 1 6 1 1 5 1 1
## text2 1 1 0 0 2 1 0 5 0 0
## text3 0 0 0 0 3 1 0 6 0 0
## text4 0 2 2 0 5 0 0 4 0 0
## text5 1 1 0 0 4 0 0 4 0 0
## text6 1 0 0 1 2 0 1 6 2 0
## [ reached max_ndoc ... 4 more documents ]
## worri get normal moment , concern
## 0.232792583 0.373032657 0.724992745 0.794280751 0.109629444 0.731038706
## corona . health even
## 1.040263180 0.004928755 0.625289832 0.894135144
## Document-feature matrix of: 1,152 documents, 260 features (87.51% sparse) and 0 docvars.
## features
## docs worri get normal moment , concern corona
## text1 0.2334374 0.7478470 0.7269987 0.7966347 0.6606898 0.7330729 1.044419
## text2 0.2334374 0.3739235 0 0 0.2202299 0.7330729 0
## text3 0 0 0 0 0.3303449 0.7330729 0
## text4 0 0.7478470 1.4539975 0 0.5505748 0 0
## text5 0.2334374 0.3739235 0 0 0.4404598 0 0
## text6 0.2334374 0 0 0.7966347 0.2202299 0 1.044419
## features
## docs . health even
## text1 0.02655109 0.6268836 0.8970996
## text2 0.02655109 0 0
## text3 0.03186130 0 0
## text4 0.02124087 0 0
## text5 0.02124087 0 0
## text6 0.03186130 1.2537672 0
## [ reached max_ndoc ... 1,146 more documents, reached max_nfeat ... 250 more features ]
Arithmetic operations with text representations
| doc_id | worri | get | normal | moment | make | feel | anxious |
|---|---|---|---|---|---|---|---|
| text1 | 0.2334374 | 0.7478470 | 0.7269987 | 0.7966347 | 1.2764132 | 0.3510523 | 0.4604796 |
| text2 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text3 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text4 | 0.0000000 | 0.7478470 | 1.4539975 | 0.0000000 | 0.0000000 | 0.5265784 | 0.0000000 |
| text5 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text6 | 0.2334374 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.5265784 | 0.4604796 |
| text7 | 0.4668748 | 0.3739235 | 0.7269987 | 0.0000000 | 0.6382066 | 0.7021046 | 0.4604796 |
| text8 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text9 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.5265784 | 0.4604796 |
| text10 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text11 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text12 | 0.2334374 | 1.1217706 | 0.7269987 | 0.0000000 | 0.0000000 | 0.5265784 | 0.0000000 |
| text13 | 0.2334374 | 0.3739235 | 0.0000000 | 0.7966347 | 0.0000000 | 0.1755261 | 0.9209592 |
| text14 | 0.4668748 | 0.7478470 | 0.0000000 | 0.0000000 | 0.6382066 | 0.0000000 | 0.0000000 |
| text15 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text16 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text17 | 0.0000000 | 0.7478470 | 0.0000000 | 0.7966347 | 0.0000000 | 0.0000000 | 0.0000000 |
| text18 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text19 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text20 | 0.0000000 | 1.8696176 | 0.7269987 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text21 | 0.0000000 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text22 | 0.0000000 | 0.0000000 | 0.7269987 | 0.7966347 | 0.0000000 | 0.0000000 | 0.0000000 |
| text23 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text24 | 0.2334374 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.0000000 | 0.9209592 |
| text25 | 0.2334374 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text26 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text27 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text28 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.5265784 | 0.4604796 |
| text29 | 0.7003122 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.9209592 |
| text30 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text31 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text32 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text33 | 0.4668748 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.3510523 | 0.4604796 |
| text34 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text35 | 0.2334374 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text36 | 0.7003122 | 0.0000000 | 0.7269987 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text37 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.0000000 | 0.0000000 |
| text38 | 0.0000000 | 0.0000000 | 0.7269987 | 0.0000000 | 0.6382066 | 0.1755261 | 0.0000000 |
| text39 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text40 | 0.2334374 | 0.3739235 | 0.7269987 | 0.7966347 | 0.0000000 | 0.1755261 | 0.0000000 |
| text41 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.5265784 | 0.0000000 |
| text42 | 0.0000000 | 0.3739235 | 0.7269987 | 0.0000000 | 0.6382066 | 0.1755261 | 0.0000000 |
| text43 | 0.7003122 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text44 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text45 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text46 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text47 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text48 | 0.0000000 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.7021046 | 0.9209592 |
| text49 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text50 | 0.0000000 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.1755261 | 0.0000000 |
| text51 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text52 | 0.0000000 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.3510523 | 0.0000000 |
| text53 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text54 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text55 | 0.0000000 | 1.1217706 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text56 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text57 | 0.0000000 | 0.0000000 | 0.7269987 | 0.7966347 | 0.0000000 | 0.5265784 | 0.4604796 |
| text58 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text59 | 0.4668748 | 0.7478470 | 0.0000000 | 0.0000000 | 0.6382066 | 0.5265784 | 0.9209592 |
| text60 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.6382066 | 0.3510523 | 0.0000000 |
| text61 | 0.4668748 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 1.3814388 |
| text62 | 0.0000000 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text63 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text64 | 0.7003122 | 2.2435411 | 0.7269987 | 0.0000000 | 1.9146198 | 0.3510523 | 0.4604796 |
| text65 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.5265784 | 0.0000000 |
| text66 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.0000000 | 0.0000000 |
| text67 | 0.7003122 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text68 | 0.0000000 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text69 | 0.4668748 | 0.0000000 | 0.7269987 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text70 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text71 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text72 | 0.4668748 | 0.0000000 | 0.7269987 | 0.0000000 | 0.0000000 | 0.3510523 | 0.4604796 |
| text73 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text74 | 0.2334374 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text75 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text76 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.6382066 | 0.1755261 | 0.4604796 |
| text77 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.5265784 | 0.4604796 |
| text78 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text79 | 0.0000000 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text80 | 1.4006245 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text81 | 0.7003122 | 0.7478470 | 1.4539975 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text82 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.5265784 | 0.0000000 |
| text83 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.1755261 | 0.0000000 |
| text84 | 0.2334374 | 0.7478470 | 0.7269987 | 0.0000000 | 0.6382066 | 0.0000000 | 0.0000000 |
| text85 | 0.0000000 | 0.0000000 | 0.0000000 | 1.5932693 | 0.6382066 | 0.3510523 | 0.0000000 |
| text86 | 0.9337497 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text87 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text88 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.3510523 | 0.0000000 |
| text89 | 0.4668748 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
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| text1115 | 0.7003122 | 0.7478470 | 0.7269987 | 0.0000000 | 0.0000000 | 0.3510523 | 0.4604796 |
| text1116 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.9209592 |
| text1117 | 0.7003122 | 0.0000000 | 0.0000000 | 1.5932693 | 0.0000000 | 0.7021046 | 0.0000000 |
| text1118 | 0.0000000 | 1.8696176 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.4604796 |
| text1119 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1120 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text1121 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text1122 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text1123 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.5265784 | 0.0000000 |
| text1124 | 0.2334374 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1125 | 0.4668748 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.1755261 | 0.4604796 |
| text1126 | 0.2334374 | 0.0000000 | 0.7269987 | 0.7966347 | 0.0000000 | 0.1755261 | 0.0000000 |
| text1127 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.4604796 |
| text1128 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text1129 | 0.2334374 | 0.0000000 | 0.7269987 | 0.0000000 | 0.0000000 | 0.3510523 | 0.4604796 |
| text1130 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.8776307 | 0.4604796 |
| text1131 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text1132 | 0.0000000 | 0.3739235 | 0.0000000 | 0.7966347 | 0.6382066 | 0.3510523 | 0.9209592 |
| text1133 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1134 | 0.0000000 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text1135 | 0.0000000 | 0.0000000 | 0.0000000 | 0.7966347 | 0.0000000 | 0.3510523 | 0.4604796 |
| text1136 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.1755261 | 0.0000000 |
| text1137 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.7021046 | 0.0000000 |
| text1138 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1139 | 0.4668748 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1140 | 0.0000000 | 0.7478470 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1141 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.3510523 | 0.4604796 |
| text1142 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1143 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1144 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.3510523 | 0.0000000 |
| text1145 | 0.9337497 | 0.0000000 | 0.0000000 | 1.5932693 | 0.6382066 | 0.1755261 | 0.4604796 |
| text1146 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 0.6382066 | 0.1755261 | 0.0000000 |
| text1147 | 0.2334374 | 0.3739235 | 0.0000000 | 0.0000000 | 0.0000000 | 0.5265784 | 0.0000000 |
| text1148 | 0.4668748 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1149 | 0.2334374 | 0.3739235 | 0.7269987 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1150 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 |
| text1151 | 0.2334374 | 0.0000000 | 0.0000000 | 0.0000000 | 1.9146198 | 0.3510523 | 0.4604796 |
| text1152 | 0.7003122 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.8776307 | 0.4604796 |
Suppose we have got two vectors:
Uses Pythagorean theorem.
For two 2-dimensional locations:
Thus:
\(c = \sqrt{a^2 + b^2} = \sqrt{9 + 1} = 3.16\)
For \(n\) dimensions:
\(d(\mathbf{x}, \mathbf{y}) = \sqrt{\sum_{i=1}^n (x_i - y_i)^2}\)
\(\text{cosine similarity}(\mathbf{A}, \mathbf{B}) = \frac{A \times B}{\sqrt{A \times A} * \sqrt{B \times B}}\)
Note: \(A \times B\) is the dot product of the vector.
V1 = c(4,2,3)
V2 = c(1,3,1)
cossim = function(A, B){
numerator = sum(A*B)
denominator = sqrt(sum(A*A))*sqrt(sum(B*B))
cosine_sim = numerator/denominator
return(cosine_sim)
}
cossim(V1, V2)## [1] 0.7278603
# Euclidean distance-based
dist(matrix(c(dfm_tfidf_df[1, 2:ncol(dfm_tfidf_df)]
, dfm_tfidf_df[2, 2:ncol(dfm_tfidf_df)])
, nrow = 2
, byrow = T)
, method = 'euclidean')## 1
## 2 7.746157
# Cosine distance-based
1 - cossim(A = dfm_tfidf_df[1, 2:ncol(dfm_tfidf_df)]
, B = dfm_tfidf_df[2, 2:ncol(dfm_tfidf_df)])## [1] 0.8857499